Into a unit square you drop two needles (having negligible width) of lengthL. (0 < L < sqrt(2)). Consider the probabilityp( L ) that they will intersect. A moment's thought reveals that the probability approaches zero as Lapproaches zero. p( L )is a strictly increasing function and approaches a limit as L approaches sqrt (2).

What is the maximum value of p( L )?

Clue

Spoiler

This is as much a logic puzzle as a mathematical one.

Inspired by BMAD's Pickup Sticks puzzle, I ask the following related question.

Into a unit square you drop two needles (having negligible width) of length

. (0 <L< sqrt(2)). Consider the probabilityL(p) that they will intersect. A moment's thought reveals that the probability approaches zero asLapproaches zero.L(pis a strictly increasing function and approaches a limit asL )approaches sqrt (2).LWhat is the maximum value of

(p?L )Clue

This is as much a logic puzzle as a mathematical one.

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